parameterization of the graph $y=x^2$ from (-2,4) to (1,1)

Question

I need to integrate a vector field over C which is described as the graph $y=x^2$ from (-2, 4) to (1, 1). Do I treat $y=x^2$ as a line segment from (-2, 4) to (1, 1), so that the parameterization is $$<-2+3t, 4-3t>$$ for $t\in[0,1]$?

Answer 1

The easiest way is to let $ x=t$ and $ y= t^2$ for $-2\le t \le 1$

The parametrization that you have introduced does not consider the curve as a parabola.

Answer 2

Any function graph $y = f(x)$ can be parametrized as $(x,f(x))$ with $x\in\cdots$.